1. Field of the Invention
This invention relates to nuclear magnetic resonance (NMR) apparatus for examining an object such as a patient by measuring a density or a relaxation time of a specific atomic nucleus, e.g., a proton. The invention relates more particularly to a quadrature detection circuit for the NMR apparatus.
2. Description of the Prior Art
It is difficult to directly observe a nuclear magnetic resonance signal, because a resonance occurs at relatively high frequencies and any frequency differences which may be of interest are very small in comparison. Accordingly, it is convenient to view a spin system as if one of the spin resonances is stationary, i.e., in a frame of resonance rotating at the same frequency. Practically, this is done in the NMR receiver by demodulating the NMR signals with a reference frequency which is chosen to be close to or equal to the resonance frequency. The resultant detected output is then the frequency difference between the spin resonance and the reference, which will be typically in the audio frequency range and can easily be observed and measured.
The phase of the spins is an angle describing the direction in which the resultant spin magnetization is pointing relative to the effective direction of the reference frequency in the rotating frame. The zero phase reference is arbitrary, though it is frequently chosen to be the direction in which all the spins point immediately after the initial radio frequency (rf) excitation pulse. A spin at right angles to this will be at 90-degrees phase, or .pi./2 radians. For a signal resonating exactly at the reference frequency the phase will be constant, but for other spin resonance frequencies the phase will be continually changing. This appears as an oscillating amplitude of the detected signal with a maximum signal obtained when the spin phase is the same as the reference, zero when there is a 90-degree phase difference, and negative when at 180 degrees from the reference. For this reason, this method of detection is known as phase sensitive detection. The quadrature detection circuit performs the signal detection relative to both a zero phase reference and a 90-degrees phase reference which is a complete description of the spin movement in the transverse plane.
Thus, the quadrature detection circuit produces a signal of twice the single phase detection power by adding both 0-degree and 90-degree phases of the demodulated signals. Accordingly, this quadrature circuit reduces noise power by a factor of 2, thereby increasing the signal-to-noise ratio by .sqroot.2.
In conventional quadrature, an NMR signal u(t) from a receiver coil of an NMR apparatus is demodulated with the respective reference signals d.sub.c and d.sub.s of the same frequency, but whose phases are different by 90 degrees. Thus, two demodulated signals u.sub.c (t) and u.sub.s (t) are extracted from the NMR signal u(t) as follows: EQU u.sub.c (t)=G.sub.c u(t)d.sub.c (t) (1) EQU u.sub.s (t)=G.sub.s u(t)d.sub.s (t) (2)
where the reference signals d.sub.c and d.sub.s are described as follows: EQU d.sub.c (t)=A.sub.c cos (2.pi.f.sub.0 t+.phi..sub.c) (3) EQU d.sub.s (t)=A.sub.s cos (2.pi.f.sub.0 t+.phi..sub.s) (4)
and G.sub.c and G.sub.s are gains of the demodulation circuit and A.sub.c and A.sub.s are amplitudes of the reference signals d.sub.c and d.sub.s, f.sub.0 is a frequency of the reference signals d.sub.c and d.sub.s, .phi..sub.c and .phi..sub.s are the phases of the respective reference signals d.sub.c and d.sub.s.
If the amplitude A.sub.c is equal to A.sub.s, and the phase difference between .phi..sub.c and .phi..sub.s is exactly 90 degrees, the quadrature circuit will produce the correct demodulated signals u.sub.c (t) and u.sub.s (t).
However, it is difficult to make the amplitudes A.sub.c and A.sub.s of reference signals d.sub.c and d.sub.s exactly equal and the phase difference between the same 90 degrees. Such amplitude and phase errors cause a ghost image to be generated overlying the image of the object being observed.